Breast cancer is the most commonly diagnosed cancer in women. Early diagnosis, which is critical for favorable clinical outcomes, is complicated by the difficulty of detecting small tumors. One physical property that clearly distinguishes healthy from cancerous tissue is mechanical stiffness (hardness). For this reason, palpation has long been used for early screening. Researchers have attempted to combine external mechanical stimulation and Magnetic Resonance Imaging (MRI) to quantitatively measure the Young's modulus (i.e., stiffness) of tissue throughout both the breast and the prostate. This technique, Magnetic Resonance Elastography (MRE), has been called "palpation at a distance." The most challenging technical issue associated with MRE is the solution of the "inverse problem," i.e., quantitatively inferring Young's modulus from MRI-measured tissue displacement data. The specific aim of this project is to develop methods and devices for enhancing breast cancer detection and diagnosis using MRE. To achieve this aim, we will develop analytical solution techniques to improve the efficiency and robustness of the inverse problem solution and design and implement a realistic clinical system.